World number one Serena Williams defeated US 15th seed Sloane Stephens 6-4, 6-1 to reach the US Open quarter-finals, as third-seeded Agnieszka Radwanska - Williams' Polish opponent in last year's Wimbledon final - lost in straight sets.

Williams' victory over Stephens on Monday (AEST) avenges the loss that ousted her from this year's Australian Open.

The defending champion won eight of the last nine games to advance after 87 minutes to a last-eight match-up against Spanish 18th seed Carla Suarez Navarro, who upset German eighth seed Angelique Kerber 4-6, 6-3, 7-6 (7-3).

"It will be a tough match," Williams said.

Williams, who at 31 could become the oldest US Open women's champion, and Stephens had not played since the 20-year-old prodigy beat the four-time US Open champion 3-6, 7-5, 6-4 in an Australian Open quarter-final last January.

"It definitely felt like a bigger match because Sloane is such a great player, but I had to stay focused in the moment," Williams said.

"I just tried the whole time to do what I wanted to, stay calm and stay relaxed."

The Williams-Stephens relationship was strained after Stephens accused the 16-time grand slam champion of being disrespectful and using intimidation tactics and mind games with her yells of "Come on", but both women said before the match that soured feelings had been repaired.

In the match, both apologised to each other for wind-blown ball tosses that they did not hit. And when they met at the net after match point, Williams told Stephens, "I love you so much."

Stephens said she was simply outplayed by the world's best.

"I thought I played good. I played pretty solid," Stephens said.

"The second set got away from me a little bit. She's number one for a reason.

"She played pretty well herself. She did a lot of things well. All in all, she did great. I played well. That's all you can do."

The showdown of American stars, the world number one and the second-highest-rated American player, came in windy conditions at Arthur Ashe Stadium.

Williams missed three early break points against Stephens but finally broke through for a 4-2 lead with a forehand service winner return that prompted a quick fist pump from the top seed.

But Williams surrendered a break on a double fault in the next game and Stephens held to level the first set at 4-4, saving a break point with a forehand winner in the process.

Williams held and then broke to win the opening set after 52 minutes, finally winning an 18-point game when Stephens swatted a forehand wide.

In the second set, Williams broke for a 3-1 lead when Stephens netted a baseline forehand and the defending champion never relented from there.

Radwanska upset by Makarova

Makarova struck a barrage of groundstroke winners to topple Radwanska 6-4, 6-4 in the fourth round at Louis Armstrong Stadium.

Radwanska started brightly, surging to a 4-0 lead in the first, but Makarova peeled off eight straight games to take the set and a 2-0 lead in the second.

Radwanska fought her way back, holding four break points to level the second set 4-4.

Makarova, the 24th seed, sealed the game with an ace before going on to close out the match in one hour and 32 minutes leaving Radwanska out of the quarter-finals at a major for the first time this year.

The 25-year-old Russian will play her first quarter-final at the US Open after twice reaching the last eight at the Australian Open.

"It feels amazing, I really love this tournament," she said.

Makarova, whose last-eight run has matched her best grand slam showings from the past two Australian Opens, next faces Chinese fifth seed Li Na, who beat Serbian ninth seed Jelena Jankovic 6-3, 6-0.